The Missing Link : The Effect of Customers on the Formation of Relationships Among Producers in the Multiplex Triads

This paper develops a concept of a "multiplex triad," i.e., a triplet composed of actors playing different roles and interconnected by different kinds of relationships. An example of such triad is a social structure comprising two producers connected via horizontal relationships and a customer connected to producers via vertical ties. Multiplex triads are important drivers of network evolution, but their dynamics remains poorly understood. Although conventional wisdom suggests that horizontal ties between producers are driven solely by their prior interactions, we find that vertical ties drive the formation of horizontal relationships in a multiplex triad. We also find that these triads are affected by the agency of the customers who (a) force producers into horizontal relationships with those producers that have protected the customers' interests in the past and (b) prevent closure in triads containing strong horizontal relationships because of the divergent objectives of these triads' members. By drawing attention to the existence of multiplex triads and their underlying dynamics, this paper advances a novel view on transitivity incorporating conflicting interests and agencies of actors within social systems.